Spatial dynamics of water and nitrogen management in irrigated agriculture.

Irrigated agriculture constitutes approximately 70% of global freshwater consumption. While the nearly 260 million hectares of irrigated land worldwide currently provide 40% of the global food supply, future expansion and intensification is likely necessary to meet a predicted 40% to 45% increase in food demand by the year 2025 (United Nations Environment Program 1999), implying additional stress on a scarce natural resource. (1) Irrigated agriculture is also a major source of groundwater nitrate pollution. Violations in the maximum allowable levels of nitrates in drinking water are reported in every European county, while African nitrate loads in some suburban groundwater wells are six to eight times World Health Organization acceptable levels. A survey of nearly 200,000 U.S. water sampling records found that more than 2 million people drank water exceeding federal nitrate standards, and nearly 52% of the community water wells and 57% of the domestic wells are considered nitrate contaminated (Nolan et al. 1998). In California, nitrates are responsible for more well closures than any other chemical, and 10% to 15% of the water supply wells violate federal standards (Bianchi and Harter 2002). (2)

In response to the potential health threats from nitrates in groundwater, a variety of regulations on irrigated agriculture have been proposed and implemented, including limits on fertilizer usage and nitrate concentrations in groundwater (Shortle and Abler 2001). Research addressing the groundwater nitrate problem has often focused on policies targeting the nitrogen input (e.g., Choi and Feinerman 1995; Nkonya and Featherstone 2000); understandably so given that annual fertilizer use, which has been estimated to add 7 billion pounds more nitrogen than is taken up by the plants on the field, has increased since the 1990s (National Research Council 1993; USDA 2005). Yet as highlighted in research by Helfand and House (1995) and Larson, Helfand, and House (1996) in a static field-level analysis of lettuce production, the complementarity between applied water rates and nitrate pollution is such that a second-best approach consisting of a water surcharge is only marginally less efficient than an emissions charge, albeit substantially more efficient than a nitrogen input charge. An added benefit from a water surcharge is a reduction in applied water, an underpriced, oversubsidized resource subject to a substantial literature of its own (Caswell, Lichtenberg, and Zilberman 1990). The complementarity between water, a scarce natural resource, and nitrates, an environmental quality problem, demonstrates the need to consider water and nutrient management policies jointly, as stressed in Lee (1998), and the potential for cross-policy effects, as shown in Weinberg and Kling (1996) for water markets and drainage policy.

Dynamic analysis of water and nitrogen inputs, crop yield, and nitrate emissions is quite limited (Segarra et al. 1989; Vickner et al. 1998). Furthermore, an issue of longstanding concern in the agronomic, soil science, and agricultural engineering literatures is field-level spatial variability in soil and irrigation system parameters (Nielsen, Biggar, and Erh 1973; Seginer 1978). While this variability has several consequences, the main implication is that irrigation water is typically distributed nonuniformly over a field with consequent impact on water infiltration, soil/plant processes, crop yields, deep percolation flows, and nitrogen leaching. Although this topic has seen only modest attention by agricultural economists, it is invariably critical when considered. In particular, Berck and Helfand (1990) show that von-Liebig-type production functions at the plant-level integrate to smooth nonlinear functions at the field level. Feinerman, Letey, and Vaux (1983) show theoretically that spatial variability typically increases profit-maximizing applied water rates, while Letey, Vaux, and Feinerman (1984) demonstrate that optimum water applications under spatial variability can differ by factors of two or more compared to uniform applications and more closely correspond to observed behavior. Similarly, Dinar, Letey, and Knapp (1985) establish that field-level spatial variability is critical to accurately analyzing salinity and drainage problems associated with irrigated agriculture. Finally, Larson, Helfand, and House (1996) express caution in policy instrument choice without more research on the variance of nitrate leaching due to field-level heterogeneity, while Chiao and Gillingham (1989) incorporate nonuniformity for applied phosphorous in dry land production.

Within the water-nitrogen economics literature, the only study to incorporate dynamic spatial variability is Vickner et al. (1998) with spatial variability defined as the fraction of a field under- or overirrigated relative to a water requirement. They conclude that ignoring irrigation application variability understates nitrate abatement policies. Their model of nonuniform irrigation differs from models typical of the irrigation economics literature, and results in some 95% of land area uniformly overirrigated and hence represented by a single parameter. (3) Somewhat contrary to Helfand and House (1995) and Larson, Helfand, and House (1996), they find that nitrogen control is a preferable second-best strategy to controlling applied water. Further analysis of this problem therefore seems crucial to natural resource usage and the environment in irrigated agriculture. (4)

This article further explores spatial heterogeneity, dynamic optimization, and nitrate emissions in irrigated agriculture with attention toward water-nitrogen complementarity and possible cross-policy effects. A spatial dynamic model of water and nitrogen management is developed with endogenous water and nitrogen applications and interseasonal nitrogen carryover. This model extends the irrigation and nitrogen economics literature by characterizing water infiltration with a spatial density function over the field. A major task is estimation of a plant-level model for yield, carryover, and emissions, where the function must exhibit appropriate global properties to account for water infiltration above and below mean levels. To this end, data from an unusually rich field trial are used to estimate a production function system exhibiting thresholds, plateau maximums, and input substitution.

Fundamental properties of the dynamic system are investigated, including decision rules, spatial moments, and evolution of the soil nitrogen spatial density function. A key finding is rapid convergence to a steady-state under a wide variety of initial conditions, which is significant for regional policy analysis as it simplifies needed computations and data. Specification tests are conducted for spatial variability and dynamic optimization; consistent with previous literature, spatial variability is fundamental for water scarcity and environmental quality degradation in irrigated agriculture. The effects of a range of water and nitrogen emission prices are evaluated also. There is a significant policy-relevant response from water and nitrogen management alone, even while crop and irrigation system are fixed. As in Johnson, Adams, and Perry (1991), the implication is that significant resource conservation and environmental quality improvement is possible at relatively low cost to agricultural productivity, at least starting from current conditions. The results also exhibit large cross-policy effects complementing Larson, Helfand, and House (1996) and Weinberg and Kling (1996).

Bioeconomics of Field-Scale Crop Growth and Management

Spatial dynamics of field-level water and nitrogen management is analyzed. Water is distributed nonuniformly over the field in response to soil heterogeneity and/or nonuniform irrigation systems, implying spatially variable water uptake and nitrogen uptake and emissions. (5) Interseasonal carryover dynamics for soil nitrogen are also considered. With variability in the various driving factors, soil nitrogen also exhibits heterogeneity over time even with initial soil nitrogen uniformity. Field-scale crop yield and emissions in each period are an integration over the field; hence, spatially variable water infiltration directly impacts current crop yield and nitrogen emissions, and indirectly affects future levels by inducing soil nitrogen variability. The importance of spatial variability and dynamics in water and nitrogen management is analyzed along with input pricing policies for water conservation and water quality at the field level.

Letting r denote the discount rate and T the planning horizon, the present value of net benefits to land and management ($/ha) is

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where t is time [years], [[bar.y].sub.t] = field-scale crop yield [Mg/ha], [[bar.w].sub.t] = field-average applied water depth [cm], [[bar.n].sub.at] = applied nitrogen [kg/ha], and [[bar.n].sub.et] = nitrogen emissions/leaching [kg/ha]. Parameters are [p.sub.y], [p.sub.w], and [p.sub.n] as the prices of crop [$/Mg], water [$/ha/cm], and nitrogen [$/kg], respectively; [kappa] is nonwater and nonnitrogen production costs associated with the cropping system [$/ha], and [p.sub.e] is nitrogen leaching cost [$/kg].